# SAT Math 2

#### Frank measured the amount of liquid that evaporated over a 12-day periodÂ fromÂ his container with lÂ equaling ounces of liquid. At the end of the day too, it had lost 3 ounces. At the end of day seven, anÂ additional 6 ounces. By the end ofÂ day 12, the container hadÂ lost one-third of what remained at the end of day seven. Which of the following represents the remaining amount of liquid in ounces in Frank's container at the end of day 12?

If l is the ounces of liquid and we're wanting to know how much was lost at the end of day 12, then we must start with what was lost at the end of day 7 (the 3 ounces from day 2+the 6 ounces from day 7 for a total of 9 ounces lost). So we have l-9, but we also know that at the end of day 12, the remaining amount is one-third of that total. So divide l-9 by 3, and Answer 3 is the only correct choice.

#### AnÂ entertainment superstore is running a special sale on DVDs and Blu-ray. DVDs (d) are priced at $8 during the sale while Blu-ray (b) are priced at $15. Each price point is a 20% reduction off the regular price. The sale pulls in $1,250 with 60 total units sold. During a regular day, DVDs and Blu-ray combine for around $800 in total sales while moving two-thirds the number of units on the special sale day. Solving which of the following systems of equations will reveal d and bÂ sold during a regular day?

Since the problem is asking for the numbers of d and b on a regular sale day, Answer 1 is the only choice that rings true. d+b=40 (number of combined units) and 10d with $10 being the regular price of DVDs while $18.75 is the regular price of Blu-ray adding up to $800.

#### Blake earns base pay of $10 per hour at a clothing boutique. He also earns a certain percentage commission on sales. Blake worked an average of 37 hours per week over a two-week period. If he also helped broker $7,500 in sales and his total pay is $1,000 for the two-week period, approximately what percentage commission does he earn?Â

He earned $740 in base pay and $260 in commission on $7,500 of sales. Approximately 3.5% is $260. Answer 3 is correct.

#### IfÂ ^{(C+x)}_{x-3}=^{x+8}_{3}, which of the following could be an expression of C in terms of x?

STEP ONE. Cross-multiply. STEP TWO. Add -3x to both sides, thus isolating C. STEP THREE. Multiply both sides * 1/3 to simplify 3C to C. STEP FOUR. Break down the quadratic equation (x+6)(x-4). Answer 3.

#### Larry wants to complete a marathon in under 6 hours, but he knows he can't run the 26.2 miles the whole way. He'll need to run (r) and walk (w). If he is able to walk at four miles per hour and run at six miles per hour, which system of inequalities shows his total running and walking time?

Using the process of elimination, you can dismiss B, C, and D, right away because the run-walk values are reversed. Answer 1 is the correct choice.

#### In a crossbow manufacturing facility, a quality control expert tests a randomly selected group of 1000 crossbows. If the expert finds 17 of the randomly selected crossbows are defective, which of the following inferences would be most supported?

If 17 of the 1,000 are defective, that translates to around 1.7%. Read the statements carefully, and Answer 2 is the only one that is true.

#### If ^{-19}_{6}<-4z+7<^{-13}_{6}, what is the greatest possible integer value of 16z-28?

STEP ONE. Multiply -4 to change the middle expression to 16z-28. STEP TWO. Don't forget to reverse inequality signs. STEP THREE. Convert the two fractions bookending the inequality. STEP FOUR. Look at the options. You want the highest possible integer value to fit the expression. You know 16z-28 is higher than 10 and 11, but it can't be 13, so that leaves Answer 3.

#### Which of the following ordered pairs (j,k) is the solution to the system of equations below?Â

-12-4j=6k

4+^{7}_{4}k=^{-8}_{7}j

Simply plug in the pairs to both equations and get two true statements. Answer 4 is the correct choice.

#### In the expressionÂ ^{76}_{123y-5y}=1, what is the value of y?

STEP ONE. Cross-multiply to get rid of the unwieldy fraction.
STEP TWO. Set common denominators of 3y for the left side of the equation and subtract, leaving you with ^{-3}_{3y}, or ^{-1}_{y}.
STEP THREE. Cross-multiply again to isolate y.
STEP FOUR. Divide both sides of the equal sign by 7.
Answer 1 is the correct choice.